( 388 ) 



As 



we find 



a:(2) (.., y) = Ck{.v, 5) a: (5, !j) d^ 





 ao f 'K ff ..(x) (fXv) 



^(2) (.., y) = ^-r/, (y) Ki^) (.^., z) r/, [z) dz = 2 ' ^ [l '^ ^ 



and there is with given x and positive e such a number tfiat for 

 7i- greater than that number and a^i/'^h we have 



})-\-m 



fM.v)ff,{y)\ 



1, 1 <«• 



i:~ 



If q ^ 0, tlien as a matter of course 



"+"'| 7..(.r)7,(^ ); 



<^ 



Let ff^O and (/{'t) be such a function of «, that tor «>() we have 



/7(«) 



besides 



then we tind 



|^(«)| ^ M and 

 J «'+-^ 







«l+'l - 



-J<iV, 



c/<( = ^4 ; 



V I ^v 1 2+7 J 



and consequently the series 



'+° 



.'/ 



<N 



converges absolutely and for constant x uniformly in (//, ((). So if 

 f{y) is a continuous function of y and if m ^ 0, »ve tind : 



I da I ^i.i:,yM)jl!/)dy — ^(f ,(.6') j f/ I'M'M/ \ ' 



A 





,1+0 



du 



n 



and therefore 



7n b b 



ldal^j{.ty,u)f{y)dy — ^^q ^v)iq..{y}f{y)dy\ 



